Relative Formulation of Physical Laws

Abstract

In Chap. 7 we described the procedures that in special relativity allow us to derive the physical laws relative to an inertial frame starting from their 4-dimensional formulation and vice versa. Determining analogous procedures in general relativity is a more difficult task. In this chapter, we analyze reasonable criteria leading to the relative formulation of physical laws starting from their 4-dimensional formulation. By this approach we determine the momentum equation and the energy equation of a material point relative to an arbitrary frame of reference starting from the four-dimensional momentum–energy equation. Then we compare the obtained equation with similar equations proposed in the literature. Finally, the above procedure is applied to derive the relative charge conservation, Maxwell’s equations, and the balance equations of an incoherent fluid (For the content of this chapter, see the review paper [142]).